CBSE Class 7 Mental Maths Perimeter And Area Worksheet - Free Printable

Certainly! Below is the complete solution to all 8 questions from your "Perimeter and Area" worksheet, with clear explanations for each.

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Question 1

> One of the sides and the corresponding height of a parallelogram are 5 cm and 3 cm respectively. Find the area of the parallelogram.

Solution:

We use the formula:
> Area of a Parallelogram = base × corresponding height

Here, base = 5 cm, height = 3 cm

So,
> Area = 5 cm × 3 cm = 15 cm²

✔ Answer: 15 cm²

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Question 2

> In a triangle, if one side is 7 cm and its corresponding height is 4 cm, find its area.

Solution:

We use the formula:
> Area of a Triangle = ½ × base × corresponding height

Base = 7 cm, height = 4 cm

So,
> Area = ½ × 7 × 4 = ½ × 28 = 14 cm²

✔ Answer: 14 cm²

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Question 3

> If area of ΔABC is 49 cm² and its height AD is 7 cm, find BC.

Solution:

In triangle ABC, if AD is the height to base BC, then:

> Area = ½ × base × height

Let base BC = *x* cm

Given: Area = 49 cm², height = 7 cm

So,
> 49 = ½ × x × 7
> 49 = (7x)/2
> Multiply both sides by 2:
> 98 = 7x
> x = 98 ÷ 7 = 14 cm

✔ Answer: BC = 14 cm

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Question 4

> If area of a parallelogram is 17.6 cm² and its base is 4 cm, find its corresponding height.

Solution:

Use:
> Area = base × height

Given: Area = 17.6 cm², base = 4 cm

So,
> 17.6 = 4 × height
> height = 17.6 ÷ 4 = 4.4 cm

✔ Answer: 4.4 cm

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Question 5

> Find the breadth of a rectangular plot if its area is 440 cm² and length is 22 cm. Also find its perimeter.

Solution:

Use:
> Area of Rectangle = length × breadth

Given: Area = 440 cm², length = 22 cm

So,
> 440 = 22 × breadth
> breadth = 440 ÷ 22 = 20 cm

Now, find perimeter:
> Perimeter = 2 × (length + breadth)
> = 2 × (22 + 20) = 2 × 42 = 84 cm

✔ Answers: Breadth = 20 cm, Perimeter = 84 cm

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Question 6

> The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.

Solution:

Use:
> Perimeter = 2 × (length + breadth)

Given: Perimeter = 100 cm, length = 35 cm

So,
> 100 = 2 × (35 + breadth)
> Divide both sides by 2:
> 50 = 35 + breadth
> breadth = 50 - 35 = 15 cm

✔ Answer: 15 cm

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Question 7

> The length and breadth of a rectangular plot are in the ratio of 4 : 3. If the perimeter is 140 cm, find its area.

Solution:

Let length = 4x cm, breadth = 3x cm

Perimeter = 2 × (length + breadth) = 2 × (4x + 3x) = 2 × 7x = 14x

Given: Perimeter = 140 cm

So,
> 14x = 140
> x = 140 ÷ 14 = 10

Therefore:
- Length = 4x = 4 × 10 = 40 cm
- Breadth = 3x = 3 × 10 = 30 cm

Now, Area = length × breadth = 40 × 30 = 1200 cm²

✔ Answer: 1200 cm²

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Question 8

> The length and breadth of a rectangular park are in ratio 9 : 5. If its perimeter is 280 m, find its area.

Solution:

Let length = 9x m, breadth = 5x m

Perimeter = 2 × (length + breadth) = 2 × (9x + 5x) = 2 × 14x = 28x

Given: Perimeter = 280 m

So,
> 28x = 280
> x = 280 ÷ 28 = 10

Therefore:
- Length = 9x = 9 × 10 = 90 m
- Breadth = 5x = 5 × 10 = 50 m

Area = length × breadth = 90 × 50 = 4500 m²

✔ Answer: 4500 m²

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## ✔ Final Answers Summary:

1. 15 cm²
2. 14 cm²
3. 14 cm
4. 4.4 cm
5. Breadth = 20 cm, Perimeter = 84 cm
6. 15 cm
7. 1200 cm²
8. 4500 m²

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